1. Find the probabilities for the following discrete random variables
a. Among a shipment of 5,000 tires, 1,000 are slightly blemished.If one purchases 10 of these tires, what is the probability that 3 or less (P (x
b. The probability that a hockey game will go into overtime is .3; Of the next 12 hockey games, what is the probability that more than 3 (P(x >3)) will go into overtime?
c. The probability that a person, living in a certain city, owns a dog is estimated to be 0.3.Find the probability that the tenth person randomly interviewed in that city is the sixth one to own a dog.
d. A local drugstore owner knows that, on average, 100 people per hour stop by his store. Find the probability that in a given 3 minute period, more than 5 (P(x > 5) people enter the store.
e. An electronic switching device occasionally malfunctions and may need to be replaced.It is known that the device is satisfactory if it makes, on average no more than .2 errors per hour.A particular five hour period is chosen as a "test" on the device. If no more than 1 error occurs, the device is considered satisfactory.What is the probability that a satisfactory device will be mis- diagnosed as "unsatisfactory" on the basis of the test?
f. A restaurant chef prepares a tossed salad containing, on average, 5 vegetables per day. Find the probability that the salad contains more than 5 vegetables on i) a given day and on ii)3 of the next 4 days?